Lowell Davis

What do sphere packing, cryptography, and Fermat’s Last Theorem all have in common? They’re all connected to modular forms, a class of complex analytic functions which satisfy an infinite number of symmetry relations. In my talk, I’ll be discussing the definitions and basic results in the study of modular forms. We’ll explore the group of matrices used to define these symmetries and talk about one particular modular form called the Eisenstein Series. We’ll also look at the Valence Formula which is a theorem closely related to, and proved using, the Residue Theorem from complex analysis.
Further, we’ll look at what the Valence Formula implies about the structure of modular forms as vector spaces.